Final answer:
The probability that Matt and Lisa will be chosen as president and vice president from the Art Club's 15 members is 1/105.
Step-by-step explanation:
The probability that two particular people are chosen for the roles of president and vice president from a group can be calculated by determining the likelihood that each is chosen for either position and then multiplying these probabilities together.
For the art club, assuming Matt and Lisa are among the 15 members, the probability that Matt will be chosen as president is 1/15. Once Matt is chosen, there are 14 members left, so the probability that Lisa is chosen as vice president is 1/14. Conversely, if Lisa were chosen first for president, the probability would still be 1/15, and then the probability that Matt is chosen as vice president would be 1/14. As these are two separate scenarios, we add the probabilities together:
Probability (Matt and Lisa are chosen) = Probability (Matt as President and Lisa as Vice President) + Probability (Lisa as President and Matt as Vice President)
= (1/15) * (1/14) + (1/15) * (1/14)
= 2/210, which simplifies to 1/105.
The probability that Matt and Lisa are chosen for the two roles is therefore 1/105.